Will attention based networks prevail over RNN and LSTM?
I think there are two parts to answering this question.

First, about the specific paper that has been mentioned.

The paper's title is hyperbolic, and probably written that way to get more people to read it. The paper itself does not make the claim that attention-based networks will supplant existing recurrent network architectures. Instead, it makes a more modest claim that the new attention-based architecture can outperform existing modes on a machine translation task (which is supported with experiments), and that, maybe, in the future, attention-based models could work well in other domains, or provide advantages in interpretability. 

However, there's also a second way to interpret this question. Attention-based networks are getting a lot of buzz in the AI community this year and to some extent last year. It seems likely that there are a lot of research efforts underway to apply them to other kinds of problems. If these efforts pan out, then they could indeed become the tool of choice.

At this point however, the answer to whether they will has to be "Maybe". There is no good underlying theory for why some NN architectures work better than others on a given kind of problem. We have post-hoc explanations for some (like, for instance, CNNs), but in the absence of a general theory, we're better off waiting for the empirical results before making a call. In particular, the No Free Lunch Theorem tells us that if Attention-based networks work very well on one kind of problem, we should actually expect them to work poorly on others! I suspect we'll have a better answer to this question in 1-2 more years however.